The expression assuming property calling sequence evaluates the expression under the assumption property on all names in expression.

The expression %assuming property is the inert form of assuming and returns unevaluated, with the expression and the related assumptions encapsulated within the %assuming structure. This permits, for instance, to compute with different conditions on the same variable or expression, all appearing within the same worksheet, each of them represented by %assuming structures with different conditions. All of is, coulditbe, simplify, diff and int commands know about these %assuming structures, that can be activated when desired using the value command.

The property parameter can be a type, inequation, or other property to be assumed on a name or expression involving names.

Note: Computations performed using assuming do not affect computations performed before or after calling assuming.

An assuming clause can be included in the condition of an if, elif, while, or until clause. In the latter case, to avoid a syntactic ambiguity, the entire condition, including the assuming clause, must be enclosed in parentheses.

$\mathrm{sqrt}\left(a^2\right)\mathbf{assuming}0<a$

$a$

$\mathrm{sqrt}\left(a^2\right)$

$\sqrt{a^2}$

$\mathrm{e1}≔\ln \left(\exp \left(-k\left[1\right]t\right)\right)$

$\mathrm{e1}≔\ln \left({\&ExponentialE;}^{-k_{1}t}\right)$

$\mathrm{e1}\mathbf{assuming}\mathrm{real}$

$-k_{1}t$

$\mathrm{e1}$

$\ln \left({\&ExponentialE;}^{-k_{1}t}\right)$

$\mathrm{e2}≔\ln \left(\frac{y}{x}\right)-\ln \left(y\right)+\ln \left(x\right)$

$\mathrm{e2}≔\ln \left(\frac{y}{x}\right)-\ln \left(y\right)+\ln \left(x\right)$

$\mathrm{simplify}\left(\mathrm{e2}\right)\mathbf{assuming}x::\mathrm{positive}$

$0$

$\mathrm{simplify}\left(\mathrm{e2}\right)\mathbf{assuming}y::\mathrm{positive}$

$\ln \left(\frac{1}{x}\right)+\ln \left(x\right)$

$\mathrm{simplify}\left(\mathrm{subs}\left(x=-x\&comma;\mathrm{e2}\right)\right)\mathbf{assuming}x::\mathrm{posint},y::\mathrm{posint}$

$2\mathrm{I}\mathrm{\pi }$

$\mathrm{about}\left(x\right)\&colon;$

x:
  nothing known about this object

$\mathrm{about}\left(y\right)$

y:
  nothing known about this object

$\mathrm{e3}≔\mathrm{Int}\left(\exp \left(-ux\right)x^{\frac{1}{3}}\&comma;x=0..\mathrm{\infty }\right)$

$\mathrm{e3}≔{\int }_0^{\mathrm{\infty }}{\&ExponentialE;}^{-ux}{x}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\&DifferentialD;x$

$\mathrm{value}\left(\mathrm{e3}\right)\mathbf{assuming}0\le u$

$\frac{2\mathrm{\pi }\sqrt{3}}{9\mathrm{\Gamma }\left(\frac{2}{3}\right)u^{\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}$

$\mathrm{value}\left(\mathrm{e3}\right)\mathbf{assuming}u<0$

$\mathrm{\infty }$

$\mathrm{\%assuming}\left(\left[\mathrm{sqrt}\left(\mathrm{`^`}\left(a\&comma;2\right)\right)\right]\&comma;\left[\mathrm{`<`}\left(0\&comma;a\right)\right]\right)$

$\sqrt{a^2}\mathbf{assuming}0<a$

$\mathrm{value}\left(\right)$

$a$

$\left(\mathrm{\%assuming}\left(\left[\mathrm{sqrt}\left(\mathrm{`^`}\left(a\&comma;2\right)\right)\right]\&comma;\left[\mathrm{`<`}\left(0\&comma;a\right)\right]\right)\right)+\left(\mathrm{\%assuming}\left(\left[\mathrm{sqrt}\left(\mathrm{`^`}\left(a\&comma;2\right)\right)\right]\&comma;\left[\mathrm{`<`}\left(a\&comma;0\right)\right]\right)\right)$

$\left(\sqrt{a^2}\mathbf{assuming}0<a\right)+\left(\sqrt{a^2}\mathbf{assuming}a<0\right)$

$\mathrm{value}\left(\right)$

$0$

$f≔x\mapsto \mathrm{sqrt}\left(a^2\right)+x$

$f≔x\mapsto \sqrt{a^2}+x$

$f\left(1\right)\mathbf{assuming}0<a$

$\sqrt{a^2}+1$

$\mathrm{Physics}:-\mathrm{Setup}\left(\mathrm{assumingusesAssume}=\mathrm{true}\right)$

$\left[\mathrm{assumingusesAssume}=\mathrm{true}\right]$

$f\left(1\right)\mathbf{assuming}0<a$

$a+1$

$\mathrm{Physics}:-\mathrm{Setup}\left(\mathrm{assumingusesAssume}=\mathrm{false}\right)$

$\left[\mathrm{assumingusesAssume}=\mathrm{false}\right]$

$f\left(1\right)\mathbf{assuming}0<a$

$\sqrt{a^2}+1$

$\mathrm{assume}\left(0<a\right)$

$f\left(1\right)$

$\mathrm{a~}+1$

For detailed information including:

How to evaluate expressions under assumptions applied to specific variables

Detailed information on how the assuming command computes under assumptions

How to use the assuming command in conjunction with the assume command

see the assuming/details help page.

The assuming command was updated in Maple 2017.